Would like to install a water filter

more than likely the saddle valve...the valve you or the plumber installed to tie into the water line and shut it off for filter install. it's getting clogged up. Turn it all the way off and on again 3 or 4 times this should clean out the little hole feeding thru the valve from the pipe.
hope this helps.
take a look here...pics of a saddle valve.

https://www.doityourself.com/forum/electric-large-kitchen-home-appliances/395295-ge-refrigerator-freezer-no-water-flow-ice-maker.html

You guys probably have water with lots of sediment in it.
Install a larger sediment filter on the line going in to the refrigerator or even better to install one at the point of entry to your house.

A whole house sediment filter will make sure that all water coming into the house is free of particulate matter. This will make your water using appliances like the refrigerator filter, dishwasher, water softener, faucet aerators...etc last way longer.



WECO BB 10SED Big Blue Water Filter System for Sediment Filtration

Pre-filter and carbon block filter are changed annually. The membrane is only changed every 3-7 years depending on water quality coming in, TDS and usage. Fourth filter is an in-line carbon filter that goes on the line up to the RO faucet.
RJH2O

Hello,

The first thing to do if you already haven't is replace the filter,it's in the grill/kickplate below the freezer door. If you have relpaced filter,need to pull refrig from wall and check that their is good water pressure from house plumbing,if it is good the water valve the sends water to icemaker&door dispenser when water is called for is going to be the problem.The part # for that valve is 4389177 it could be purchased at your local appliance parts store on oline at;
searspartsdirect.com
apdepot.com
repairclinic.com
assuredparts.com

The filter BUT NOT the water valve could be purchased locally at Sears,Lowe's or Home Depot

I hope this helps you to diagnose your icemaker/dispenser
Gene

Do not use a steel or plastic braided supply line. They make the ice taste bad.

See if it works when you pull the filter out and try running it (without the filter in). If it works, try buying a new filter and make sure you have the filter that is made for your specific refrigerator. If no water comes out or no ice is made after pulling filter out, than you probably have a obstruction in the line. If thats the case you should have someone come out to fix it. If your mechanically inclined you can try to do it yourself. I would suggest reading the owners manual first, in the "troubleshooting" section.

My parents frig had the same problem. The steel tabs that hold the filter in place are very small and frail. Heres what I did to solve the problem, at least temporarily. While firmly holding the filter release button, gently bend the tabs together using an extra long pair of curved needle nose pliers.

Call the manufacture or get a new fridge.

could be a water solenoid problem (at the back portion where water from the sink enters ), or a micro switch in the dispenser area problem.

also, check if u have a water filter. could be clogged already.

tnx 4 using fixya,

drcool

Just replace GE's filter with a standard inline filter that hooks to 1/4" water line tubing. Sounds like their filter has no flow rate either...
Here's a popular one:
http://cgi.ebay.com/AICRO-GAC-IN-LINE-FILTER-2-X-10-X-1-4-FNPT-JG-FIT-/390180520853?pt=LH_DefaultDomain_0&var=&hash=item99ab36a9be#ht_500wt_721